Simulating signal integrity structures

Abstract

Disclosed are system and methods for simulating signal integrity structures using stable processed modes (e.g., matched traveling-wave power modes), and/or for creating response surfaces from stable response parameters.

What is claimed is: 
     
       1. A computer-implemented method of simulating a signal integrity structure excitable via transmission lines, the method comprising the steps of:
 (a) constructing by a processor and storing in memory coupled to the processor, a plurality of stable processed modes for the signal integrity structure, each stable processed mode comprising a linear combination of a plurality of eigenmodes, the construction of each stable processed mode comprising: (i) computation of at least one of a first matrix T and a second matrix U, the first matrix T being computed by integrating electric fields of the eigenmodes over a first path between a corresponding terminal and a reference terminal and the second matrix U being computed by integrating magnetic fields of the eigenmodes over a second path around the corresponding terminal; (ii) computation of a transformation matrix R using at least one of the first matrix T and the second matrix U, and (iii) modifying the eigenmodes using the transformation matrix R to obtain the stable processed mode; and 
 (b) computationally simulating by the processor the signal integrity structure using the plurality of stable processed modes. 
 
     
     
       2. The method of  claim 1  wherein the stable processed modes comprise matched terminal modes. 
     
     
       3. The method of  claim 2  wherein the matched terminal modes comprise travelling wave power modes. 
     
     
       4. The method of  claim 2  wherein the matched terminal modes comprise at least one of current modes or voltage modes. 
     
     
       5. The method of  claim 1  wherein constructing the stable processed modes comprises simulating the transmission lines to construct eigenmodes, and computationally processing the eigenmodes to obtain the stable processed modes. 
     
     
       6. The method of  claim 1  wherein computationally simulating the signal integrity structure comprises providing an input signal, the simulation returning an output signal based on the input signal. 
     
     
       7. The method of  claim 6  wherein providing the input signal comprises computationally exciting a stable processed mode at an interface of the signal integrity structure with the transmission lines. 
     
     
       8. The method of  claim 6  further comprising characterizing the signal integrity structure by at least one parameter indicative of a relationship between the input signal and the output signal. 
     
     
       9. The method of  claim 8  wherein the at least one parameter comprises at least one of a terminal scattering parameter, a terminal admittance parameter, or a terminal impedance parameter. 
     
     
       10. The method of  claim 8  further comprising de-embedding the at least one parameter. 
     
     
       11. The method of  claim 8  further comprising renormalizing the at least one parameter. 
     
     
       12. The method of  claim 8  further comprising varying at least one design variable of the signal integrity structure and repeating steps (a) and (b) for the varied design variable. 
     
     
       13. The method of  claim 12  wherein the at least one design variables comprises at least one of a material property, a geometric variable, or an operating frequency of the signal integrity structure. 
     
     
       14. The method of  claim 12  wherein repeating steps (a) and (b) comprises tracking at least some of the stable processed modes while varying the at least one design variable. 
     
     
       15. The method of  claim 14  further comprising determining, based at least in part on the tracked stable processed modes, a functional dependence of the at least one parameter on the at least one design variable. 
     
     
       16. The method of  claim 15  wherein determining the functional dependence comprises interpolating the at least one parameter between multiple values of the at least one design variable. 
     
     
       17. The method of  claim 16 , further comprising at least one of de-embedding or renormalizing the at least one parameter subsequent to the interpolation. 
     
     
       18. The method of  claim 15  further comprising graphically representing the functional dependence on a display device. 
     
     
       19. The method of  claim 8  further comprising graphically representing the at least one parameter. 
     
     
       20. The method of  claim 1  wherein at least one of steps (a) and (b) is based at least in part on a finite element method. 
     
     
       21. A computer-implemented method of characterizing the physical behavior of a signal integrity structure excitable via transmission lines and interfacing with the transmission lines at a plurality of ports, the method comprising:
 (a) for each of a plurality of values of a design variable of the signal integrity structure, the values being received in memory coupled to a processor: (i) computationally exciting by the processor a plurality of incoming eigenmodes as input signals at the ports, the computational excitation of the plurality of incoming eigenmodes comprising: (i) computation of at least one of a first matrix T and a second matrix U, the first matrix T being computed by integrating electric fields of the eigenmodes over a first path between a corresponding terminal and a reference terminal, and the second matrix U being computed by integrating magnetic fields of the eigenmodes over a second path around the corresponding terminal; (ii) computation of a transformation matrix R using at least one of the first matrix T and the second matrix U, and (iii) modifying the eigenmodes using the transformation matrix R to obtain the plurality of incoming eigenmodes (ii) computationally simulating by the processor the signal integrity structure to determine a plurality of outgoing modes as output signals at the ports, and (iii) computationally determining by the processor at least one stable parameter based on the input signals that are the incoming eigenmodes and the output signals that are the outgoing modes, the at least one stable parameter comprising a parameter that is: (i) based on the input signals and output signals, and (ii) post processed according to a transformation matrix; and 
 (b) interpolating the at least one stable parameter between different values of the design variable to determine a functional dependence of the at least one stable parameter on the design variable, thereby characterizing the behavior of the signal integrity structure in terms of input and output, wherein the at least one stable parameter is tracked between the different values of the design variable. 
 
     
     
       22. The method of  claim 21  wherein the incoming eigenmodes comprise matched terminal modes. 
     
     
       23. The method of  claim 22  wherein the incoming eigenmodes comprise at least one of travelling wave modes, current modes, or voltage modes. 
     
     
       24. The method of  claim 21  wherein determining the at least one stable parameter comprises determining first parameters indicative of a relationship between the input and output signals, and processing the first parameters to obtain the stable parameters. 
     
     
       25. The method of  claim 21  wherein the at least one stable parameter is a terminal parameter. 
     
     
       26. The method of  claim 21  further comprising:
 (c) post-processing the at least one interpolated stable parameter for user-selected values of the design variable. 
 
     
     
       27. The method of  claim 26  wherein post-processing comprises at least one of deembedding or renormalizing the at least one interpolated stable parameter. 
     
     
       28. A system for simulating a signal integrity structure excitable via transmission lines, comprising:
 (a) a memory for storing data representative of the signal integrity structure and the transmission lines; and 
 (b) at least one simulation module, in communication with the memory, for simulating the transmission lines to construct a plurality of stable processed modes and for simulating the signal integrity structure using the plurality of stable processed modes, each stable processed mode comprising a linear combination of a plurality of eigenmodes, the construction of each stable processed mode comprising: (i) computation of at least one of a first matrix T and a second matrix U, the first matrix T being computed by integrating electric fields of the eigenmodes over a first path between a corresponding terminal and a reference terminal, and the second matrix U being computed by integrating magnetic fields of the eigenmodes over a second path around the corresponding terminal; (ii) computation of a transformation matrix R using at least one of the first matrix T and the second matrix U, and (iii) modifying the eigenmodes using the transformation matrix R to obtain the stable processed mode. 
 
     
     
       29. A system for characterizing the physical behavior of a signal integrity structure excitable via transmission lines, comprising:
 (a) a memory for storing data representative of the signal integrity structure for a plurality of values of a design variable of the signal integrity structure; 
 (b) a simulation module, in communication with the memory, for simulating the signal integrity structure and to determine at least one stable parameter based on the simulation, the at least one stable parameter comprising a parameter based on stable processed modes, each stable processed mode comprising a linear combination of a plurality of eigenmodes, the linear combination being computed using a transformation matrix R, or a parameter based on eigenmodes that is post processed according to a transformation matrix the transformation matrix R being generated by computing at least one of a first matrix T and a second matrix U, the first matrix T being computed by integrating electric fields of the eigenmodes over a first path between a corresponding terminal and a reference terminal, and the second matrix U being computed by integrating magnetic fields of the eigenmodes over a second path around the corresponding terminal; and 
 (c) an interpolation module, in communication with the memory, for interpolating the at least one stable parameter between different values of the design variable to determine a functional dependence of the at least one stable parameter on the design variable, whereby the behavior of the signal integrity structure is characterized in terms of input and output. 
 
     
     
       30. The system of  claim 29 , wherein the simulation uses stable processed modes. 
     
     
       31. The system of  claim 29 , further comprising a post-processing module, in communication with the memory, for at least one of de-embedding or renormalizing the at least one interpolated stable parameter. 
     
     
       32. A computer-implemented method for de-embedding a response surface of a signal integrity structure, the method comprising:
 (a) obtaining the response surface by computationally simulating by a processor the signal integrity structure for a plurality of values of at least one design variable, the values being received in a memory coupled to the processor, and computationally interpolating by the processor at least one stable response parameter resulting from the simulation, between the plurality of values, the at least one stable parameter comprising a parameter based on stable processed modes, each stable processed mode comprising a linear combination of a plurality of eigenmodes, the linear combination being computed using a transformation matrix R, or a parameter based on eigenmodes that is post processed according to a transformation matrix the transformation matrix R being generated by computing at least one of a first matrix T and a second matrix U, the first matrix T being computed by integrating electric fields of the eigenmodes over a first path between a corresponding terminal and a reference terminal, and the second matrix U being computed by integrating magnetic fields of the eigenmodes over a second path around the corresponding terminal; 
 (b) computationally interpolating by the processor a processed matrix of propagation constants associated with eigenmodes of the signal integrity structure; and 
 (c) for each of multiple user-selected values of the at least one design variable,
 (1) constructing by the processor a de-embedding matrix from (i) at least one desired deembedding distance and (ii) the processed matrix of propagation constants corresponding to the user-selected value, and 
 (2) de-embedding by the processor the response surface using the de-embedding matrix. 
 
 
     
     
       33. The method of  claim 32 , wherein the de-embedding distance corresponds to a length by which an external transmission line interfacing with the signal integrity structure is extended. 
     
     
       34. The method of  claim 32 , wherein the de-embedding matrix is constructed based, at least in part, on eigenvectors and eigenvalues of the processed matrix of propagation constants. 
     
     
       35. A system for de-embedding a response surface of a signal integrity structure excitable via transmission lines, the system comprising:
 (a) a memory for storing data representative of the response surface and propagation constants associated with eigenmodes of the transmission lines, the response surface representing a dependence of a stable response parameter on a design variable within a range of values thereof, the stable parameter comprising a parameter based on stable processed modes, each stable processed mode comprising a linear combination of a plurality of eigenmodes, the linear combination being computed using a transformation matrix R, the transformation matrix R being generated by computing at least a first matrix T and a second matrix U, the first matrix T being computed by integrating electric fields of the eigenmodes over a first path between a corresponding terminal and a reference terminal, and the second matrix being computed by integrating magnetic fields of the eigenmodes over a second path around the corresponding terminal; 
 (b) an interpolation module for interpolating a processed matrix of the propagation constants; and 
 (c) a de-embedding module that facilitates, for any user-selected value of the design variable within the range of values, de-embedding the response surface by 
 (1) constructing a de-embedding matrix from (i) at least one user-specified de-embedding distance and (ii) the processed matrix of propagation constants corresponding to the user-selected value, and 
 (2) de-embedding the response surface using the de-embedding matrix.